Near equatorial orbit small sar constellation for developing nations

IJRET: International Journal of Research in Engineering and Technology ISSN: 2319-1163
__________________________________________________________________________________________
Volume: 02 Issue: 04 | Apr-2013, Available @ http://www.ijret.org 654
NEAR EQUATORIAL ORBIT SMALL SAR CONSTELLATION FOR
DEVELOPING NATIONS
Lawal AD1
and Radice GM2
1
Researcher, 2
Dr, Aerospace Engineering, University of Glasgow, Glasgow, United Kingdom,
a.lawal.1@research.gla.ac.uk, gianmarco.radice@glasgow.ac.uk
Abstract
The need to harness the benefits of space, to help urban growth and development, using cheaper space systems has become appealing
to developing nations. The desired all weather radar satellite poses limitations on a small satellite. Several spaceborne Synthetic
Aperture Radar (SAR) satellite configurations have been proposed to overcome the significant limit on earth surface revisit time for
small SAR satellites, optimising a network of small SAR satellites dedicated to developing nations posed several challenges. In an
effort to address some of these challenges, a new concept based on a constellation of small SAR satellite network, in an almost
equatorial inclined orbit, operating in a multistatic configuration and solely dedicated to Equatorial region has been proposed. The
network consists 3 receiver-only platforms (passive satellites) flying in formation with one transmit/receiver satellite (active satellite).
Furthermore, five groundstation sites required for mission operation are located with the equatorial region. The system aims to
provide 24 hours of near-real time data, over the equatorial region. A total of two orbital planes for 8 satellites are proposed. This
report will describe the process of selecting a suitable orbit constellation configuration. It also determines the stability of the relative
motion between the satellites within the formation in order to ensure the desired image product is consistent during operations.
Furthermore, it also discusses the process of selecting suitable groundstation locations for the mission operations
Index Terms: Near Equatorial orbit, SAR, Interferometry Pendulum, constellation
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1. INTRODUCTION
The desire to acquire near-real time, high resolution images
independent of weather conditions has always been appealing
to scientific and commercial industries. The need for a
sophisticated system for monitoring a region such as the
Equatorial Region (ER), with diverse types of valuable
resources cannot be overemphasised. Within the ER1
, is a host
of developing nations, who stand to benefit scientifically,
commercially and educationally from the implementation of
an all-weather remote sensing system. Typical SAR satellites
payloads are characterised by large volume, high power
demand, and complexity. These, impacts on launch and
mission costs, which can be unaffordable by developing
nations. Recent missions have demonstrated the use of SAR
payloads on smaller satellites, but there still stands a huge cost
implication when a constellation of SAR satellites is
considered.
The vast amount of natural resources such as animal,
agricultural and human resources within the ER, can be
assumed to be underutilised by harbouring nations which are
mainly developing countries. In order to speed-up the
development within this region, an approach entailing state-of-
the-art technology implementation is suggested. This approach
requires abundance of affordable data, which can be processed
for resources management and urban development. In view of
the high cost implications of SAR missions, reduction of
mission cost becomes paramount to ensure potential member
states with ER can afford either the launch, space or ground
segment costs. The concept revolves around the collaboration
of several resident nations with the ER on a Multistatic SAR
network mission. The geographical location of all ground
segments will be within the ER region. The operation and
maintenance of all mission resources will be conducted by
resident nation’s member of staff. The collaboration is
designed to build confidence amongst each nation, in their
ability to manage these resources, while enhancing
development. One method of making space missions
affordable is the use of small satellites to for throughput
comparable to big systems.
The growing interest from the scientific community, in the
application of distributed SAR systems has been ably
demonstrated by the in-orbit operations of both TerraSAR-X
and Tandem-X in a twin satellite formation called the helix
[6]. Consequently, the concept of implementing a multistatic
SAR system that operates solely within the ER is considered
the first step towards realising an ambition for providing
affordable space mission to developing nations. In addition to
acquisition of typical monostatic data products, this multistatic
network will conduct interferometry operations capable for
delivering a variety of data product depending on satellite
configuration.

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Several spaceborne radar systems employing two or more
receivers on separate platforms are commonly known as a
multistatic SAR system [2]. The basic form of such a system
is a Bistatic configuration, consisting of two receivers on
separate platforms. The application areas of multistatic SAR
configuration include but not limited to, single pass across-
track interferometry, single pass along-track interferometry,
wide swath imaging, ground target moving indication (GTMI),
spaceborne tomography, interference suppression, multistatic
imaging and resolution enhancement [3]. It is evident that
developing nations can immensely benefit from the
availability of data provided by a multistatic SAR system,
potentially serving as “spring board” for regional
development.
Therefore, to design a low-cost SAR constellation mission,
this paper refers to the use of a multistatic SAR constellation
network in a “semi-active” configuration. The constellation is
made up of transmit/receiver (monostatic SAR) satellite and
several receiver-only (passive SAR) satellites orbiting around
a define region. The monostatic satellite (Tx/Rx) is regarded
as the master and labelled M01 and M11, while the passive
satellites (Rx) are regarded as slaves and labelled S01, S02,
S03 for slave plane one and S11, S12,and S13 for slave plane
2 respectively. The semi-active configuration allows the use of
receiver-only satellites that whose payload can be fitted on
microsatellite (typical 100kg), thereby eliminating high power
demands which impact positively on satellite electric power
subsystem sizing [12].
To this end, this paper aims to describe the orbit design
process and the ground segment location selection process
required for implementing an almost equatorial inclined LEO
orbiting Multistatic SAR network
2. ORBIT DESIGN
The requirement for a system capable of providing 24 hours of
NRT data of the equatorial region, informed the selection of
an initial orbit inclination of 10 degrees. This ensures that the
satellite groundtrack periodically moves between ±10 degrees
latitude per orbit. The power demand per orbit per satellite is
an area that needs to be considered. It is envisage that the
technological advances in improving the conversion
efficiencies of solar cells to about 40 percent [7] will help
keep the satellite size at minimum since less area would be
required for power generation. The satellites will be located in
the LEO at an altitude of approximately 700km to prevent the
Van Allen belt, and ensure rapid revisit times over the region
of coverage. A semi-active configuration
2.1 Constellation
The selected choice for achieving the ER coverage
requirement considered existing satellite formations. The first
formation considered was the famous cartwheel formation, a
concept introduced for the SAR interferometric application
with the ENVISAT mission [9]. Similar to the original
concept where 3 passive satellites were proposed to image the
area of the Earth illuminated by Envisat SAR, each master
satellite is allocated three slave satellites for collecting
returned echoes of signals transmitted by the master satellite.
A total of two orbital planes are used for the constellation:
Plane one is called the “master plane” and consists of two
master satellites evenly separated in time. Both master
satellites share the same orbital parameters and hence have the
same semi-major axis, eccentricity, inclination and (RAAN).
The distance between both satellites is a result of selecting
different arguments of latitude (assuming a circular orbit) for
each master satellite.
Plane two is regarded as the “slave plane” which
accommodates six slave satellites. Similar to the original
cartwheel concept, all slave satellites share a semi-major axis,
inclination and RAAN with the master satellites. However, all
slave orbits are similar with slight eccentricities, with each
argument of perigee symmetrically displaced (n satellites
differ by in argument of perigee).
Originally it was proposed that initial position along the orbit
selected for the master satellite should be several kilometres
away in order to achieve safe distance. This configuration
relies on frequently orbit maintenance manoeuvres beyond the
scope of this paper. A major benefit of this configuration is the
availability of varying baseline distances well suited for
conducting SAR interferometry (InSAR). The elliptic relative
motion experienced by the slave satellites ensures baselines
are achieved in both the along-track (target velocity
measurements) and across-track (target topography)
interferometry. Figure 1 shows a typical cartwheel formation
consisting of one master and 3 slaves. The figure is viewed
from outer space over the Earth’s North Pole.
Fig -1: Typical cartwheel configuration view over the North
Pole
The interferometric cartwheel formation is typified by the
coupling between the vertical cross-track (radial) separation

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and the along-track displacement. An independent
optimization of along-track baselines for several applications
becomes impossible due to coupling between both spacecraft
axis [13]. The formation hardly provides stable across-track
baselines. Figure 2 illustrates a representative formation
assumed for monitoring the ER as viewed from outer space
through the polar axis.
Fig -2: Orbital configuration for the SAR network using the
cartwheel formation
The effects of orbit perturbation on the cartwheel formation is
characterized by identical J2 secular effects, implying the
ascending node and perigee precession affects all satellite
equally. However, there is a secular and slow in-plane and
out-plane drift experience between the master satellite and
slave satellites when in cartwheel formation. The secular plane
drift requires continuous orbital correction economically
achievable when master satellite conducts this manoeuvre.
The cartwheel formation can also be modified so that in
addition to offsetting the argument of perigee of each orbit
(eccentricity vectors), the various inclinations and RAAN also
differ. This results in an inclined ellipse which is independent
of the orbital plane of master satellite’s orbit. The true angular
positions of the each satellite can then be chosen as ,
which yields a uniformly distributed number of slave satellites
along the ellipse. This formation is characterised by constant
horizontal baseline which is well suited for ground moving
target indication (GMTI) and geolocation applications [5].
The second and selected formation considered, provides
multiple baselines at fixed baseline ratio along the entire orbit
cycle [10, 11]. The effects of a large baseline manifests in the
sensitivity to across-track interferometry, which is well suited
in application areas such as digital elevation model (DEM)
generation. On the other hand, short baselines are most useful
for assisting in phase unwrapping, when data of undulating
areas such as valleys is involved [5]. This formation is often
referred to as the pendulum formation, which the original
concept involved three slave satellites with the same
inclination but different ascending nodes and a master satellite
with a different inclination from the slave satellites. All
satellites are in circular orbit and hence have equal velocities.
The concept demonstrated the use of highly inclined orbits
where satellite orbits cross at the northern and southern turn.
To prevent potential collision, and enhance safe operation, a
slight offset to the eccentricity vector is applied. This ensures
vertical separation at the point the orbits cross, with the in-
plane separation capable of providing cross-track
interferograms at the Polar Regions [11]. The along –track
baseline can always be varied depending on application, by
moving the satellite along the orbit to provide GMTI or ocean
current mapping [14]. Large along-track baselines can be used
for measuring slow movements such as sea vessels, while
short along-track baselines can be used for higher velocities
such as traffic monitoring. The pendulum formation is plagued
by the fact that it requires additional fuel for station keeping of
the formation [5].
The major distinction between the original concept and the
approach taken in this paper is that the orbits will only cross at
the Equator, hence no interferograms of the polar region with
be generated. The formation also differs since it consists of
one master satellite dedicated to three slave satellites each.
More importantly, is that two master satellites share the same
orbital plane, but are separated in time (orbital period/2).
Similarly, the slave satellites also share the same orbital plane
and inclination but different RAAN.
One set of slave satellites (three) are dedicated to one master
satellite and the other set are separated in time (orbital
period/2) from the first set. The slave satellites are ahead of
the master satellites for safe operation, and in event that the
orbits cross at the equator, the altitude of the slave satellite
would be lower than the master satellite due to different
ballistic coefficients. Figure 3 and 4 illustrate 2D and 3D the
application of the pendulum configuration for a near
equatorial orbit using Satellite Tool Kit (STK) software.
Fig -3: STK 2D representation of Pendulum formation over
the Equatorial Region
It is pertinent to note that there are other configurations such
as the Carpe not discussed in this paper. The Carpe is a

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combination of the cartwheel and pendulum configuration
where the satellites have the same inclination and different
RAAN. A thorough evaluation of the carpe formation and will
be evaluated in the near future.
Fig -4: STK 3D Representation of Pendulum formation over
2.2 Constellation Analysis
To conduct an initial analysis of the constellation design, the
concept of formation flying is explored in order to get an
insight of possible optimization techniques that can be
implemented. The use of multiple satellites flying in formation
with a specific geometry prevents the substantial financial and
technical challenges of building a radar dish of equivalent size
[16]. Although formation flying involves two concepts: one
involving two or more spacecraft docking; and spacecraft
flying in formation with the aim of maintaining relative
positions. The latter is the concept which is explored in this
work.
The spacecraft formation considered involves several satellites
of equal type and build. This ensures that each satellite ideally
has equal ballistic coefficient and therefore experience orbit
decay at a similar rate [17, 18]. Thus this assumption allows
the possibility of analytically finding closed relative orbits
[16]. The close relative orbit as seen by the spacecraft rotating
reference frame, describes a geometry that can either be
circular or elliptic. Figure 4 shows the definition of the
reference frame for satellites in close formation using just two
satellites (One master or reference satellite and one slave). In
various text reference materials [17, 18, 19], the satellites are
often referred to as “Chief and Deputy” respectively. The
formation illustrates a general type with out-of-plane relative
motion between the satellites. This reference frame is often
called the Hill reference frame (ᴏ frame), who’s origin is at the
master satellite position with vectors mathematically
expressed as
Fig -5: Hill coordinates reference frame definition for satellite
formation [19]
Where the master satellite inertia position is expressed by the
vector and the slave position expressed by vector
.The Master satellite is the satellite about which all
other (slave) satellites fly in formation and ideally appear to
orbit around it. The ᴏ frame is in the master satellite orbit
radius direction, is parallel to the orbit momentum vector
(i.e vector cross product of master satellite’s position and
velocity vectors), and completes the traid. Therefore the
relative orbit position vector ρ is expressed in the ᴏ frame as
By satisfying some constraints such as assuming a circular
orbit, the relative orbit can be bounded to ensure that the
spacecraft do not drift apart [5, 16, 17], thus leading to the
simplest form of Clohessy-Wiltshire Equations below.
Reference [16] provides the derivation of the relationship
between relative positions and orbital elements and the
constants for mapping the orbital elements to x,y,z coordinate.
The resulting equations are

__________________________________________________________________________________________
Where A0, B0, α and β are given by the differences in the
inclination, argument of perigee, and mean anomaly given by;
Using Clohessy-Wiltshire equation, a MATLAB program was
run to calculate the relative position of the slave satellites
while in a pendulum configuration. This was conducted by
using the master satellite and one slave satellite. The initial
orbital elements which had been earlier derived based on user
requirements and applications served as input into the
program. Orbital element values for master satellite are as
follows:
 Semi-major axis (a) km : 7078.14
 Eccentricity (e) : 0
 Inclination (i) deg : 10
 RAAN (Ω) deg : 0
 Argument of Perigee (ω) deg : 0
 Mean Anomaly (M) deg : 0
Orbital element differences are as follows:
 Δa: 0
 Δe: 0
 Δi: 2
 ΔΩ: 20
 Δω: 0
 ΔM: 5
Therefore slave satellite initial orbital elements were
calculated as by adding the orbital element differences and
mapping into the x,y,z coordinate system as described above.
Figure 6 is a plot of the slave relative position over 24 hours,
which shows that the relative motion is simply oscillatory in
the out-of –plane direction due to difference in inclination
angle. A maximum across-track separation of 500 km is
achievable. The in-plane distance for both x and y directions
remain constant as expected for a typical pendulum
configuration. It is duly noted that other assumptions include
the fact that Clohessy-Wiltshire equation is based on the two-
body equation and therefore the effects of perturbations is not
considered.
Fig -6: STK 3D Representation of Pendulum formation over
3. GROUND SEGEMENT DESIGN
The desire to locate all mission resources input and output
within the ER implies all ground segment are geographically
located between latitudes ±10 degrees of the Equator. The
selection of ground station locations commenced by
populating every country whose border lies within the ER and
in some cases, Islands were also considered. Table 1 is an
extract of the geographical locations of countries whose
boundaries lie within the ER. A total number of 49
countries/Islands have boundaries within the ER.
Table -1: Countries and Islands whose geographical boundary
lie with the ER

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The choice of groundstation location was based on several
criteria:
 Level of involvement in space technology
 Location of boundary within the ER
 Potential ability to afford space missions
Although several other criteria are still being evaluated, the
ones listed were required to provide baseline idea of selecting
the groundstation locations. An initial number of 12 ground
station sites were selected on the basis of ensuring overlap
between successive coverage ranges using a minimum
elevation angle of 6 degrees.
However, due to possibility of interference and need for
reduction in mission cost, the ground station locations were
reduced to 5. An access report from a simulation run over 24
hours using STK shows that there were varying access times
for each groundstation. A maximum of 14 passes and
minimum of 13 passes was experienced by each ground
station per satellite. An overall mean duration of 149 minutes
is available to each satellite for downlinking data to each
groundstation. This implies a total of 745 minutes available
each satellite in the SAR network for downlinking data to
groundstation in view.
Fig -7: STK 2D visualisation of groundstation locations masks
The groundstation locations can be varied with little or no
change in the access times, depending on interested nations;
however, an optimum configuration would require a
maximum of 5 groundstation sites. Operational strategies that
outline communication protocol and priority/ conflict
management must be defined. Data transfer methods from
archiving units of one site to the other must also be defined.
Fig -8: STK 3D visualisation of ground station location masks
3.1 Access to selected ground segment sites
As mentioned in section 1, there are over 45 countries within
the ER, with only 5 selected as possible locations for ground
segment sites. These locations are subject to flexibility
although certain criteria such as having existing space agency,
and proximity to Equator were considered.
Fig shows a Northerly oriented view of the locations of the
selected ground stations.
Fig 9: Selected locations for Ground Segment – View from
the North Pole
The distance between subsequent locations varies; however,
the maximum time between successive contacts with
groundstation must be less than 10 minutes. Table 1 details the
location of the selected ground station sites. Sites can be
flexibly selected provided the out of communication time with
satellites is less than 10 minutes.
Table 2: Location of selected ground segment sites with ER
Country Latitude Longitude
Accra 5° 30' N 0° 10' W
Cayenne 4° 56' N 52° 20'W
Mogadishu 2° 04' N 45° 22'E
Singapore 1° 17' N 103° 51'E
Tarawa 1° 19' N 172° 58'E

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Fig10: Ground segment location showing M01 making
contact with groundstation in Accra
The access to the selected ground segment location allows
each group of the satellite constellation to always be in view
of one ground station.
Fig 11: Access report of M01 to selected ground sites within
ER
Fig summarizes a daily access report for M01 to each ground
segment. A total of 70 accesses daily are available to
download captured data, or upload telecommand to each
spacecraft as required. This configuration serves to usher a
new approach in data generation.
Using a line of sight constraint of a minimum of 6 degrees
elevation angle is applied to each groundstation. Therefore,
the available downlink time translates to approximately half of
a sidereal day. Figure 11 is a 24 hours extract of the access
report in STK for M01 to Cayenne and Mogadishu.
Fig -12: Extract of access report for M01 to Cayenne and
Mogadishu over 24 hours duration
CONCLUSIONS
This paper identifies the need for a dedicated all weather SAR
system to provide continuous high quality data products to
developing nation. Developing nation form majority of the
countries with the equatorial region and therefore, the study
proposes the establishment of a consortium of developing
nations with the equatorial region solely for the realisation of a
network of small SAR satellites, whose resources are sole
dedicated to the equatorial region. The thrust of this work is to
provide a cheap and affordable solution to space mission for
developing nations.
The approach taken is a semi-active configuration consisting
of receiver only satellites in formation with traditional
monostatic SAR satellites for the acquisition of various data
products. The constellation consisting of mainly small
satellites is capable of functioning as a larger system. Two
main distributed SAR configurations were considered, and the
pendulum configuration was preferred to the cartwheel mainly
due to the variety of application areas it offers, at the expense
of additional fuel for station keeping. The pendulum formation
has never been adopted for a near equatorial LEO orbit and
therefore presents new challenges that require further
investigations.
The SAR network comprises of both space and ground
segments, with the later consisting of 5 potential groundstation
sites located at different geographical location within the ER.

__________________________________________________________________________________________
Preliminary results show that a near 24 hours data availability
is feasible with all small satellites fully operational and
serving as a “Big system”. However, resource management
procedures need to be defined in order to avoid conflict.
The approach suggests the formation of a consortium of
developing nations within the ER that could exploit
advantages such as overall reduction in cost of space mission
due to shared cost, availability of cheaper data, availability of
a variety of data products, and opportunity to apply the data
for various form of development.
Five sites were selected as locations for ground segments,
which will facilitate a nearly 24 hours availability of data with
a total of 70 access passes to the ground segments.
ACKNOWLEDGEMENTS
I would like to extend my sincere appreciation to my kids,
Moesha and Leo Lawal. The thought of ensuring you both live
in a better world spurred me on in my journey to realize new
concepts for developing nations. My undying gratitude to Dr,
Gianmarco Radice, for you kindness, patience and support all
through my time with you as a research student. To my Dad,
Abdul Lawal, your spirit never left my side as it guided me all
the way even through hard times. Finally, to all the fellow
researchers, friends and colleagues who contributed to this
work, I will forever be grateful.
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Fiedler, H. and Volker, M. (2005) Spaceborne polarimetric
SAR interferometry: performance analysis and mission
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of Polarimetry and Polarimetric Interferometry (PolInSAR),
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[5] Torres, R., Lokas, S., Moller, H.L., Zink, M. and Simpson,
D.M. (2004) The TerraSAR-L mission and system, in
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Technology. Wiley & Son, Ltd
[7] Giese, C., (2011) TANDEM-X, Presentation at the Science
Team Meeting, Astrium
[8] Martin, A et al., (2012). Solar Cell Efficiency Tables
version 39. Progress in Photovoltaics: Research and
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[10] Massonnet, D. (2001) Capabilities and limitations of the
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TerraSAR-L, ESA Fringe Workshop, Frascati, Italy.
[12] Fiedler, H. and Krieger, G. (2004) Close formation of
micro-satellites for SAR interferometry, 2nd International
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[13] Wanwiwake, T., Underwood, C. (2010) A Bi/Multi-Static
Microsatellite SAR Constellation, Small Satellite Missions for
Earth Observation, DOI 10.1007/798-3-642-03501-2, ©
Springer-Verlag Berlin Heidelberg 2010
[14] Das, A. and Cobb, R. (1998) TechSat 21 – space missions
using collaborating constellations of satellites, in 12th
AIAA/USU Conference on Small Satellites, Utah.
[15] Bethke, K.H., Baumgartner, S., Gabele, M., Hounam, D.,
Kemptner, E., Klement, D., Krieger, G. and Erxleben, R.
(2006) Air- and spaceborne monitoring of road traffic using
SAR/MTI project TRAMRAD, ISPRS J. Photogrammetry
and Remote Sensing, 61 (3–4), 243–259.
[16] H. Schaub and J. Lunkins. Analytical Mechanics of Space
Systems. AIAA Educations Series, 2003
[17] Vallado, A.D. and McClain, W.D. Fundamentals of
Astrodynamics and Applications. 3rd ed. 2007. Microsm Press
and Springer. New York. ISBN 978-1-881883-14-2
[18] Wertz, J. R. and Larson, W.J., Space Mission Analysis
and Design. 3rd ed. 2007. Microsm Press and Springer. New
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[19] H. Schaub (2002). Spacecraft Relative Orbit Geometry
Description through Orbit Element Differences. 14th U.S.
National Congress of Theoretical and Applied Mechanics
Blacksburg, VA, June 23–28
BIOGRAPHIES:
Abdul Duane Lawal is currently a
research student of the Aerospace
department of the university of Glasgow.
His previous experiences include, the
system engineer of NigeriaSat-X mission
at SSTL. He is currently researching on
distributed SAR systems.
Gianmarco Radice is a Reader at the
University of Glasgow. He is currently
the Director of space Programmes at
University of Glasgow Singapore,
Singapore Polytechnic Campus. He’s
research interest include: Space Mission
Analysis and Design, Orbit Mechanic and Astrodynamics.

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